Properties

Label 2015.1.bq
Level 2015
Weight 1
Character orbit bq
Rep. character \(\chi_{2015}(464,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 16
Newform subspaces 5
Sturm bound 224
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2015.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2015 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2015, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 8 0 0

Trace form

\( 16q - 4q^{4} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{4} - 4q^{9} - 4q^{10} - 8q^{14} + 4q^{19} - 8q^{31} - 4q^{35} - 4q^{36} + 12q^{39} + 8q^{40} + 8q^{41} - 8q^{45} - 4q^{49} - 16q^{51} + 4q^{56} + 8q^{59} + 8q^{66} + 4q^{71} - 8q^{81} + 4q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2015, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2015.1.bq.a \(2\) \(1.006\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-155}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\)
2015.1.bq.b \(2\) \(1.006\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-155}) \) None \(0\) \(2\) \(2\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\)
2015.1.bq.c \(4\) \(1.006\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)
2015.1.bq.d \(4\) \(1.006\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots\)
2015.1.bq.e \(4\) \(1.006\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$3$ (\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))
$5$ (\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T^{2} )^{2} \))
$7$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$11$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$13$ (\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T )^{4} \))(\( 1 - T^{2} + T^{4} \))(\( ( 1 - T )^{4} \))
$17$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))
$19$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))
$23$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))
$29$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$31$ (\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))
$37$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))
$41$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))
$43$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))
$47$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))
$53$ (\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 + T^{2} )^{4} \))
$59$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))
$61$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$67$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$71$ (\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))
$73$ (\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))
$79$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 + T^{2} )^{4} \))
$83$ (\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 + T )^{8} \))
$89$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$97$ (\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
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